Ninety members of the House of Representatives will start their first terms this January. That represents a fifth of the House membership. Fifty-five of the 90 new members will be Democrats, constituting more than 23 percent of the Democrats in the House. This kind of influx of new members has in the past led to major changes in House rules. The 1974 class that came into Congress during the Watergate scandal successfully challenged the committee chairmanship structure of the House that had been based almost entirely on seniority. When the Republicans took control for the first time in 40 years, in 1994, other major reforms were implemented, including eliminating proxy voting, where members give their party leader their right to vote on any matter in committee in the member’s absence. Similar changes might occur now.

There is one new element this time: President Trump has publicly pledged to try to convince Republican members to vote for a Democrat, Rep. Nancy Pelosi, D-San Francisco, for speaker, if she has any trouble reaching the required 218 relying just on Democratic members.

Pelosi immediately rejected the offer of help. However, she is being pressured by nine Democrats in the Problem Solvers Caucus to adopt new, more open rules for how the House carries on its duties; all nine have pledged not to support a candidate for speaker who does not embrace the changes. If they hold firm, Pelosi will have to gain 218 of the 227 remaining Democratic House members to become speaker again. Seventeen other Democrats have already announced they won’t support her. So, Pelosi might not be in any position to reject out of hand any Republican votes that might be offered.

Not only for her own speakership chances, but for the good of the country, Pelosi ought to reconsider the hand extended across the aisle. A speaker elected with some support from the minority party would be a visible sign of a commitment to diminishing the partisan divide of which the vast majority of Americans disapprove. Further, if Pelosi accepts the recommendations for amending the House rules to expand the rights of members who lack seniority, both parties’ junior members would benefit. It would be a refreshing opening up of the processes for making law, reforming the rules that both parties have followed when they have held the speakership in recent years.

It is natural that new members of any institution will lack influence. However, when the new members are as numerous as this new class (more than 20 percent), they have a unique opportunity to press for greater access to influence. Among the improvements they should pursue:

1. Outlaw “tithing.” Certain committees are far more sought after than others. The Ways and Means Committee writes tax laws. The Appropriations Committee passes all spending bills every year. No other committees come close to their influence. There are also second- and third-tier committees: Armed Services and Agriculture in the second, Small Business and Science, Space, and Technology in the third. To be chosen for a preferred committee, and to be chair of any committee, Members are expected to “tithe”: to contribute a specific sum from campaign funds to their party’s national congressional committee.

2. End the rule followed by both parties in the past requiring that a bill be supported by a majority of the majority party before allowed a vote. This rule kills cross-party compromise. Imagine, for instance, a bill supported by 40 percent of majority party members, and 90 percent of minority party members. Though supported by two-thirds of the House, it would not receive a vote under this rule.

3. Elect committee chairs by secret ballot of the entire committee. This will empower centrists, rather than those who are closest to a party’s leadership.

The first vote of a new member is for speaker; the second is for the rules. The new members have the chance to make their first votes their best votes.

Tom Campbell is a professor at Chapman University. He served five terms in the House, two in the minority and three in the majority. He also served in the California state Senate. He resigned from the Republican Party in 2016 and is now independent.